matlab上机完美版解析.docx

1、matlab上机完美版解析1. 已知3阶椭圆IIR数字低通滤波器的性能指标为：通带截止频率0.4，通带波纹为0.6dB，最小阻带衰减为32dB。设计一个6阶全通滤波器对其通带的群延时进行均衡。绘制低通滤波器和级联滤波器的群延时。%Q1_solution%ellip(N,Ap,Ast,Wp)/双线性法设计低通滤波器%N-The order of the filter%Ap-ripple in the passband%Ast-a stopband Rs dB down from the peak value in the passband%Wp-the passband widthbe,ae=e

2、llip(3,0.6,32,0.4);hellip=dfilt.df2(be,ae);f=0:0.001:0.4;g=grpdelay(hellip,f,2);g1=max(g)-g;b,a,tau=iirgrpdelay(6,f,0 0.4,g1);hallpass=dfilt.df2(b,a);/级联hoverall=cascade(hallpass,hellip);hFVT=fvtool(hellip,hoverall);set(hFVT,Filter,hellip,hoverall);legend(hFVT,Lowpass Elliptic filter,Compensated fil

3、ter);/添加图例的标注clear;num1,den1=ellip(3,0.6,32,0.4);GdH,w=grpdelay(num1,den1,512);plot(w/pi,GdH); gridxlabel(omega/pi); ylabel(Group delay, samples);F=0:0.001:0.4;g=grpdelay(num1,den1,F,2); % Equalize the passbandGd=max(g)-g;% Design the allpass delay equalizernum2,den2=iirgrpdelay(6,F,0,0.4,Gd);GdA,w

4、= grpdelay(num2,den2,512);hold on;plot(w/pi,GdH+GdA,r); legend(Original Filter,Compensated filter);2设计巴特沃兹模拟低通滤波器，其滤波器的阶数和3-dB截止频率由键盘输入，程序能根据输入的参数，绘制滤波器的增益响应。clear;N=input(Type in the order N = );Wn=input(Type in the 3-dB cutoff frequency Wn = ); %模拟频率num,den=butter(N,Wn,s);w=0:2*Wn;h=freqs(num,den,

5、w);plot(w,20*log(abs(h),grid;3已知系统的系统函数为：用MATLAB进行部分分式展开，并写出展开后的表达式。% Partial-Fraction Expansion of Rational z-Transformnum = 0 0 1 -0.2 0.5;den = 1 3.2 1.5 -0.8 1.4;r,p,k = residuez(num,den);disp(Residues);disp(r)disp(Poles);disp(p)disp(Constants);disp(k)4设计切比雪夫I型IIR数字高通滤波器，其性能指标为：通带波纹，最小阻带衰减，通带和阻带

6、边缘频率和绘制所设计的滤波器增益响应。%a4disp(prewapping is done,and T=2);Wp = tan(0.75*pi/2);Ws = tan(0.5*pi/2);Rp = 0.5;Rs = 43;N,Wn = cheb1ord(Ws,Wp,Rp,Rs,s);b,a = cheby1(N,Rp,Wn,s);bt,at=lp2hp(b,a,Wp);num,den=bilinear(bt,at,0.5);h,omega = freqz(num,den);plot (omega/pi,20*log10(abs(h);grid;xlabel(omega/pi); ylabel(

7、Gain);title(Type I Chebyshev Highpass Filter); clear;%预畸变Rp=0.5;Rs=43;Wp=0.75;Ws=0.35;N,Wp=cheb1ord(Wp,Ws,Rp,Rs);num,den=cheby1(N,Rp,Wp,high);w=0:pi/1024:pi;h=freqz(num,den,w);subplot(2,1,1);plot(w/pi,abs(h),grid;title(Amplitude in linear scale)subplot(2,1,2);plot(w/pi,20*log10(abs(h),grid;title(Amp

8、litude in log scale)5已知复指数序列为：，绘制30点该序列的实部和虚部。 n=0:29; x=0.2*exp(0.4+1i*0.5)*n); subplot(211); stem(n,real(x); xlabel(n);ylabel(real part); grid on; subplot(212); stem(n,imag(x); xlabel(n);ylabel(imag part); grid on;6设计切比雪夫I型模拟低通滤波器，其滤波器的阶数，3-dB截止频率和通带的波纹由键盘输入，程序能根据输入的参数，绘制滤波器的增益响应。clear;N=input( 滤波

9、器阶数N =);Wn=input( 截止频率Wn = );Rp=input(通带波纹Rp = );num,den=cheby1(N,Rp,Wn,s);w=0:5*Wn;h=freqs(num,den,w);plot(w,20*log10(abs(h),grid;xlabel(Frequency, Hz); ylabel(Gain, dB);7已知系统的系统函数为：用MATLAB求系统z变换的有理形式，并写出有理形式的表达式。r=1 0.6 1.8;p=-3.2 2.4 2.4;k=0.2;num, den = residuez(r,p,k)8设计巴特沃兹IIR数字带通滤波器，其性能指标为：归一

10、化通带截止频率为，归一化阻带截止频率为，通带波纹为0.6dB，最小阻带衰减为35dB。绘制所设计的滤波器增益响应。% Design of IIR Butterworth Bandpass FilterWp =0.4 0.6;Ws = 0.3 0.7;Rp = 0.6;Rs = 35;N,Wn = buttord(Wp, Ws, Rp, Rs);b,a = butter(N,Wn);h,omega = freqz(b,a,256);plot (omega/pi,abs(h);grid;xlabel(omega/pi); ylabel(Gain);title(IIR Butterworth Ban

11、dpass Filter);disp(N);disp(Wn);9已知指数序列为：，绘制24点该序列。 n=0:23; x=2*0.9.n; stem(n,x,.); grid on; ylabel(Amplitude); xlabel(Time index);10设计椭圆模拟低通滤波器，其滤波器的阶数，3-dB截止频率，通带的波纹和阻带衰减由键盘输入，程序能根据输入的参数，绘制滤波器的增益响应。clear;N=input(Type in the order N = );Wn=input(Type in the 3-dB cutoff frequency Wn = );Rp=input(Type

12、 in the the passband ripple Rp = );Rs=input(Type in the the minimum stopband attenuation Rs = );num,den=ellip(N,Rp,Rs,Wn,s);w=0:5*Wn;h=freqs(num,den,w);plot(w,20*log10(abs(h),grid;xlabel(Frequency, Hz); ylabel(Gain, dB);11已知系统的系统函数为：用MATLAB的impz函数求hn的前30个样本值。clc;A=1 3.2 1.5 -0.8 1.4;B=1 -0.2 0.5;H,T

13、=impz(B,A,30);disp(H);stem(T,H);12已知5阶椭圆IIR数字低通滤波器的性能指标为：通带截止频率0.35，通带波纹为0.8dB，最小阻带衰减为35dB。设计一个10阶全通滤波器对其通带的群延时进行均衡。绘制低通滤波器和级联滤波器的群延时。%ellip(N,Ap,Ast,Wp)%N-The order of the filter%Ap-ripple in the passband%Ast-a stopband Rs dB down from the peak value in the passband%Wp-the passband widthbe,ae=ellip

14、(5,0.8,35,0.35);hellip=dfilt.df2(be,ae);f=0:0.001:0.4;g=grpdelay(hellip,f,2);g1=max(g)-g;b,a,tau=iirgrpdelay(10,f,0 0.4,g1);%the first parameter above is the order of the allpasshallpass=dfilt.df2(b,a); hoverall=cascade(hallpass,hellip);hFVT=fvtool(hellip,hoverall);set(hFVT,Filter,hellip,hoverall);l

15、egend(hFVT,Lowpass Elliptic filter,Compensated filter);clear;num1,den1=ellip(5,0.8,35,0.35);GdH,w=grpdelay(num1,den1,512);plot(w/pi,GdH); gridxlabel(omega/pi); ylabel(Group delay, samples);F=0:0.001:0.4;g=grpdelay(num1,den1,F,2); % Equalize the passbandGd=max(g)-g;% Design the allpass delay equalize

16、rnum2,den2=iirgrpdelay(10,F,0,0.4,Gd);GdA,w = grpdelay(num2,den2,512);hold on;plot(w/pi,GdH+GdA,r); legend(Original Filter,Compensated filter);13编写4点滑动平均滤波器程序。原始未受干扰的序列为：sn=3n(0.8)n, 加性噪声信号dn为随机序列，幅度0.6，受干扰的序列为：xn= sn+ dn，分别绘制长度为40的原始未受干扰的序列，噪声序列和受干扰序列，以及滑动平均滤波器的输出。% Program 2_4% Signal Smoothing by

17、 a Moving-Average FilterR = 40;d = 6/5*(rand(1,R)-0.5);m = 0:1:R-1;s =3.*m.*0.8.m;x = s + d;subplot(211);plot(m,d,r-,m,s,b:,m,x,m-)title(The sequence with noise);ylabel(Amplitude)legend(dn,sn,xn);b = ones(4,1)/4;y = fftfilt(b,x);subplot(212);plot(m,s,r-,m,y,b-) title(The original sequence & the outp

18、ut sequence);legend(sn,yn);ylabel(Amplitude)14绘制长度为10点的矩形序列的16点离散傅立叶变换样本的幅度和相位。xn=ones(10,1);Xk=fft(xn,16);Xkf=abs(Xk);Xkp=angle(Xk);subplot(211);stem(0:15,Xkf,filled);xlabel(Time index/n);ylabel(Magnitude);subplot(212);stem(0:15,Xkp,filled);xlabel(Time index/n);ylabel(Phase)15已知系统的系统函数为：用MATLAB的fil

19、ter函数求hn的前20个样本值。num=1,-0.2,0.5;den=1,3.2,1.5,-0.8,1.4;x=1 zeros(1,20-1);y=filter(num, den, x);disp(Coefficients of the power series expansion);disp(y)stem(y)16利用Hermann公式估计FIR低通滤波器的阶数。该滤波器的性能指标为：通带截止频率为1500Hz，阻带截止频率为1800Hz，通带波纹为0.015，阻带波纹为0.021，抽样频率为5000Hz。% Program 10_1% Estimation of FIR Filter O

20、rder Using remezord%clear;fedge = 1500 1800 ;% input(Type in the bandedges = );mval = 1 0;%input(Desired magnitude values in each band = );dev = 0.015 0.021;%input(Allowable deviation in each band = );FT = 5000;%input(Type in the sampling frequency = );N, fpts, mag, wt = remezord(fedge, mval, dev, F

21、T);d = fdesign.lowpass(n,fp,fst,N,0.6,0.72);design(d);fprintf(Filter order is %d n,N);17编写长度为5的中值滤波器程序。原始未受干扰的序列为：sn=3n(0.8)n, 加性噪声信号dn为随机序列，幅度0.6，分别绘制长度为40的受干扰序列，以及中值滤波器的输出。% Program 2_5% Illustration of Median Filtering%N = 5;R = 40; b = 6/5*(rand(1,R)-0.5); % Generate impulse noisem = 0:R-1;s = 3

22、*m.*(0.8.m); % Generate signalx = s + b; % Impulse noise corrupted signaly = medfilt1(x,N); % Median filteringsubplot(2,1,1)stem(m,x);axis(0 50 -1 8);grid on;xlabel(n);ylabel(Amplitude);title(Impulse Noise Corrupted Signal);subplot(2,1,2)stem(m,y);grid on;xlabel(n);ylabel(Amplitude);title(Output of

23、Median Filter);18已知16点序列xn的DFT为：绘制序列xn的实部和虚部。Xk=(0:15)/16;xn=ifft(Xk);xnre=real(xn);xnim=imag(xn);subplot(2,1,1);stem(0:15,xnre,.);grid on;title(The real part of the sequence);subplot(2,1,2);stem(0:15,xnim,.);grid on;title(The imaginary part of the sequence);19已知系统的系统函数为：用MATLAB测试该系统的稳定性。num=1 -0.2

24、0.5;den=1 3.2 1.5 0.8 1.4;zplane(num,den);grid on;20. 利用Remez算法设计一个等波纹线性相位FIR低通滤波器。该滤波器的性能指标为：通带截止频率为1500Hz，阻带截止频率为1800Hz，通带波纹为0.015，阻带波纹为0.021，抽样频率为5000Hz。% Program 10_2% Design of Equiripple Linear-Phase FIR Filters%format longfedge = 1500 1800;FT = 5000;mval = 1 0;dev =0.015 0.021;N,fpts,mag,wt =

25、 remezord(fedge,mval,dev,FT);b = remez(N,fpts,mag,wt);disp(FIR Filter Coefficients); disp(b)h,w = freqz(b,1,256);subplot(2,1,1);plot(w/pi,20*log10(abs(h);grid;xlabel(omega/pi); ylabel(Gain, dB);subplot(2,1,2);plot(w/pi,20*log10(abs(h);grid;axis(0 0.4 -0.7 0.7);xlabel(omega/pi); ylabel(Gain, dB);titl

26、e(detail in passband)21. 21.已知序列，计算两个序列的卷积，并绘制序列。clc;clear;x1=2.2 3 -1.5 4.2 -1.8; x2=0.8 -1 1.6 0.8;x=conv(x1,x2) %结果在主界面输出stem(x,filled);grid on;xlabel(Time index/n);ylabel(Amplitude);title(The output convolution);22. 已知序列xn为，绘制序列xn的DFT和DTFT的幅度。n=0:15;x=cos(pi*n*0.5);X=fft(x);subplot(2,1,1);stem(n

27、,X,.);title(Magnitude of DFT)xlabel(n); ylabel(Magnitude)%circulating DTFTk=0:499;w = pi/500*k;X1=x*(exp(-1i*pi/500).(n*k);magX=abs(X1);subplot(2,1,2);plot(w/pi,magX);title(幅度响应);grid;ylabel(幅度);xlabel(以pi为单位的频率);23. 已知FIR滤波器的系统函数为：用MATLAB将系统函数分解为二次多项式之积，并写出各二次多项式的表达式。clear P=2.4,3.2,1.5,0.8,1.4,3.6

28、,5.2; r=roots(P);%调用函数计算 syms z s1=simple(z-r(1)*(z-r(2); d1=simple(s1./z2)s2=simple(z-r(3)*(z-r(4); d2=simple(s2./z2) s3=simple(z-r(5)*(z-r(6);d3=simple(s3./z2)Q=2.4*d1*d2*d324已知FIR数字低通滤波器的性能指标为：通带截止频率0.35，阻带截止频率0.45，通带和阻带波纹 = 0.01。设计满足该滤波器的Kaisers窗函数，绘制出Kaisers窗函数的增益响应。clear;fpts=0.35,0.45;mag=1,0

29、;dev=0.01,0.01;N,Wn,beta,ftype=kaiserord(fpts,mag,dev);kw=kaiser(N+1,beta);b=fir1(N,Wn, kw);h,omega=freqz(b,1,512);plot(omega/pi,20*log10(abs(h);grid;xlabel(omega/pi); ylabel(Gain, dB);25已知系统的频h响特性为： 绘制该系统的幅频特性和相频特性。cleark=500; % number of frequency samples is 500num=1 -.2 .5 2 -.6; %Numerator coefficientsden=1 3.2 1.5 -.8 1.4; %Denomin